Question

Simplify completely quantity 2 x squared plus 20 x plus 32 all over x squared minus 2 x minus 80.

Answer 1

To simplify the expression, we factored the numerator and denominator, canceled common factors, and obtained the simplified form 2(x + 2) over (x - 10).

Step-by-step explanation:

To simplify the given rational expression, 2x² + 20x + 32 over x² - 2x - 80, we need to factor both the numerator and the denominator. Factoring the numerator:

2x² + 20x + 32 = 2(x² + 10x + 16)

2(x + 8)(x + 2) (by factoring x² + 10x + 16)

Factoring the denominator:

x² - 2x - 80 = (x - 10)(x + 8)

Now the expression looks like:

2(x + 8)(x + 2)
-------------- =
(x - 10)(x + 8)

We can cancel out the common factor of (x + 8):

2(x + 2)
--------- =
(x - 10)

So, the simplified form is:

2(x + 2)
-------- = (x - 10)

Answer 2

(2x^2+20x+32)/x^2-2x-80

2(x^2+10x+16)/x^2-2x-80
2(x^2+8x+2x+16)/x^2-10x+8x-80
2[(x+8)(x+2)]/(x+2)(x-10)
2(x+8)/(x-10)